Chapter 4 Review and Practice Test

Learning objectives

Learning objectives

• Review the key ideas of this chapter.

• Apply the chapter's methods to review exercises.

• Check your understanding with a practice test.

##

Worked example

boundary line

geoboard

A geoboard is a board with a grid of pegs on it.

graph of a linear equation

horizontal line

y

intercepts of a line

x

y

linear equation

linear inequality

negative slope

A negative slope of a line goes down as you read from left to right.

ordered pair

origin

x

y

parallel lines

Lines in the same plane that do not intersect.

perpendicular lines

Lines in the same plane that form a right angle.

point–slope form

positive slope

A positive slope of a line goes up as you read from left to right.

quadrant

x

y

rectangular coordinate system

xy

rise

The rise of a line is its vertical change.

run

The run of a line is its horizontal change.

slope formula

slope of a line

slope-intercept form of an equation of a line

y

solution of a linear inequality

x

y

vertical line

x

x

x

x

x

y

y

y

y

##

Key Concepts

• Sign Patterns of the Quadrants $\begin{array}{lcclcclccl} \mathrm{Quadrant I} & & & \mathrm{Quadrant II} & & & \mathrm{Quadrant III} & & & \mathrm{Quadrant IV} \\ (x,y) & & & (x,y) & & & (x,y) & & & (x,y) \\ (+,+) & & & (-,+) & & & (-,-) & & & (+,-) \\ \end{array}$

• Points on the Axes On the x-axis, $y=0$. Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates $(a,0)$. On the y-axis, $x=0$. Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates $(0,b).$

• Solution of a Linear Equation An ordered pair $(x,y)$ is a solution of the linear equation $Ax+By=C$, if the equation is a true statement when the x- and y- values of the ordered pair are substituted into the equation.

• Graph a Linear Equation by Plotting Points Step 1. Find three points whose coordinates are solutions to the equation. Organize them in a table. Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work! Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

• Find the x- and y- Intercepts from the Equation of a Line Use the equation of the line to find the x- intercept of the line, let $y=0$ and solve for x. Use the equation of the line to find the y- intercept of the line, let $x=0$ and solve for y.

• Graph a Linear Equation using the Intercepts Step 1. Find the x- and y- intercepts of the line. Let $y=0$ and solve for x. Let $x=0$ and solve for y. Step 2. Find a third solution to the equation. Step 3. Plot the three points and then check that they line up. Step 4. Draw the line.

• Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation. If it only has one variable, it is a vertical or horizontal line. $x=a$ is a vertical line passing through the x- axis at $a$$y=b$ is a horizontal line passing through the y- axis at $b$. If y is isolated on one side of the equation, graph by plotting points. Choose any three values for x and then solve for the corresponding y- values. If the equation is of the form $ax+by=c$, find the intercepts. Find the x- and y- intercepts and then a third point.

• Find the Slope of a Line from its Graph using $m=\frac{\mathrm{rise}}{\mathrm{run}}$ Step 1. Locate two points on the line whose coordinates are integers. Step 2. Starting with the point on the left, sketch a right triangle, with the hypotenuse going from the first point to the second point. Step 3. Count the rise and the run on the legs of the triangle. Step 4. Take the ratio of rise to run to find the slope.

• Graph a Line Given a Point and the Slope Step 1. Plot the given point. Step 2. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 3. Starting at the given point, count out the rise and run to mark the second point. Step 4. Connect the points with a line.

• Slope of a Horizontal Line The slope of a horizontal line, $y=b$, is 0.

• Slope of a vertical line The slope of a vertical line, $x=a$, is undefined

• The slope–intercept form of an equation of a line with slope $m$ and y-intercept, $(0,b)$ is, $y=mx+b$.

• Graph a Line Using its Slope and y-Intercept Step 1. Find the slope-intercept form of the equation of the line. Step 2. Identify the slope and y-intercept. Step 3. Plot the y-intercept. Step 4. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 5. Starting at the y-intercept, count out the rise and run to mark the second point. Step 6. Connect the points with a line.

• Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation. If it only has one variable, it is a vertical or horizontal line.$x=a$ is a vertical line passing through the x-axis at $a$.$y=b$ is a horizontal line passing through the y-axis at $b$. If $y$ is isolated on one side of the equation, in the form $y=mx+b$, graph by using the slope and y-intercept. Identify the slope and y-intercept and then graph. If the equation is of the form $Ax+By=C$, find the intercepts. Find the x- and y-intercepts, a third point, and then graph.

• Parallel lines are lines in the same plane that do not intersect. Parallel lines have the same slope and different y-intercepts. If m${}_{1}$ and m${}_{2}$ are the slopes of two parallel lines then ${m}_{1}={m}_{2}.$ Parallel vertical lines have different x-intercepts.

• Perpendicular lines are lines in the same plane that form a right angle. If ${m}_{1}\,\mathrm{and}\,{m}_{2}$ are the slopes of two perpendicular lines, then ${m}_{1}\cdot{m}_{2}=-1$ and ${m}_{1}=\frac{-1}{{m}_{2}}$. Vertical lines and horizontal lines are always perpendicular to each other.

• To Find an Equation of a Line Given the Slope and a Point Step 1. Identify the slope. Step 2. Identify the point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 4. Write the equation in slope-intercept form.

• To Find an Equation of a Line Given Two Points Step 1. Find the slope using the given points. Step 2. Choose one point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 4. Write the equation in slope-intercept form.

• To Write and Equation of a Line If given slope and y-intercept, use slope–intercept form $y=mx+b$. If given slope and a point, use point–slope form $y-{y}_{1}=m(x-{x}_{1})$. If given two points, use point–slope form $y-{y}_{1}=m(x-{x}_{1})$.

• To Find an Equation of a Line Parallel to a Given Line Step 1. Find the slope of the given line. Step 2. Find the slope of the parallel line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 5. Write the equation in slope-intercept form.

• To Find an Equation of a Line Perpendicular to a Given Line Step 1. Find the slope of the given line. Step 2. Find the slope of the perpendicular line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 5. Write the equation in slope-intercept form.

• To Graph a Linear Inequality Step 1. Identify and graph the boundary line. If the inequality is $\le\mathrm{or}\ge$, the boundary line is solid. If the inequality is < or >, the boundary line is dashed. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality? Step 3. Shade in one side of the boundary line. If the test point is a solution, shade in the side that includes the point. If the test point is not a solution, shade in the opposite side.

##

Review Exercises

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

Verify Solutions to an Equation in Two Variables

In the following exercises, which ordered pairs are solutions to the given equations?

Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

Recognize the Relation Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

1. ⓐ Is the ordered pair a solution to the equation?

2. ⓑ Is the point on the line?

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph each equation.

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

Identify the x- and y-Intercepts on a Graph

In the following exercises, find the x- and y-intercepts.

Find the x- and y-Intercepts from an Equation of a Line

In the following exercises, find the intercepts of each equation.

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

Use $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

Solve Slope Applications

In the following exercises, solve these slope applications.

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y=mx+b$.

Identify the Slope and y-Intercept from an Equation of a Line

In the following exercises, identify the slope and y-intercept of each line.

Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y-intercept.

In the following exercises, determine the most convenient method to graph each line.

Graph and Interpret Applications of Slope–Intercept

Use Slopes to Identify Parallel Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.

Use Slopes to Identify Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.

Find an Equation of the Line Given the Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

Find an Equation of the Line Given the Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Find an Equation of the Line Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

Find an Equation of a Line Parallel to a Given Line

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

Find an Equation of a Line Perpendicular to a Given Line

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

Graph Linear Inequalities

In the following exercises, graph each linear inequality.

##

Find the slope of each line shown.

Graph the line for each of the following equations.

Find the equation of each line. Write the equation in slope–intercept form.

Graph each linear inequality.

Key Terms

boundary line

geoboard

A geoboard is a board with a grid of pegs on it.

graph of a linear equation

horizontal line

y

intercepts of a line

x

y

linear equation

linear inequality

negative slope

A negative slope of a line goes down as you read from left to right.

ordered pair

origin

x

y

parallel lines

Lines in the same plane that do not intersect.

perpendicular lines

Lines in the same plane that form a right angle.

point–slope form

positive slope

A positive slope of a line goes up as you read from left to right.

quadrant

x

y

rectangular coordinate system

xy

rise

The rise of a line is its vertical change.

run

The run of a line is its horizontal change.

slope formula

slope of a line

slope-intercept form of an equation of a line

y

solution of a linear inequality

x

y

vertical line

x

x

x

x

x

y

y

y

y

##

Key Concepts

• Sign Patterns of the Quadrants $\begin{array}{lcclcclccl} \mathrm{Quadrant I} & & & \mathrm{Quadrant II} & & & \mathrm{Quadrant III} & & & \mathrm{Quadrant IV} \\ (x,y) & & & (x,y) & & & (x,y) & & & (x,y) \\ (+,+) & & & (-,+) & & & (-,-) & & & (+,-) \\ \end{array}$

• Points on the Axes On the x-axis, $y=0$. Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates $(a,0)$. On the y-axis, $x=0$. Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates $(0,b).$

• Solution of a Linear Equation An ordered pair $(x,y)$ is a solution of the linear equation $Ax+By=C$, if the equation is a true statement when the x- and y- values of the ordered pair are substituted into the equation.

• Graph a Linear Equation by Plotting Points Step 1. Find three points whose coordinates are solutions to the equation. Organize them in a table. Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work! Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

• Find the x- and y- Intercepts from the Equation of a Line Use the equation of the line to find the x- intercept of the line, let $y=0$ and solve for x. Use the equation of the line to find the y- intercept of the line, let $x=0$ and solve for y.

• Graph a Linear Equation using the Intercepts Step 1. Find the x- and y- intercepts of the line. Let $y=0$ and solve for x. Let $x=0$ and solve for y. Step 2. Find a third solution to the equation. Step 3. Plot the three points and then check that they line up. Step 4. Draw the line.

• Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation. If it only has one variable, it is a vertical or horizontal line. $x=a$ is a vertical line passing through the x- axis at $a$$y=b$ is a horizontal line passing through the y- axis at $b$. If y is isolated on one side of the equation, graph by plotting points. Choose any three values for x and then solve for the corresponding y- values. If the equation is of the form $ax+by=c$, find the intercepts. Find the x- and y- intercepts and then a third point.

• Find the Slope of a Line from its Graph using $m=\frac{\mathrm{rise}}{\mathrm{run}}$ Step 1. Locate two points on the line whose coordinates are integers. Step 2. Starting with the point on the left, sketch a right triangle, with the hypotenuse going from the first point to the second point. Step 3. Count the rise and the run on the legs of the triangle. Step 4. Take the ratio of rise to run to find the slope.

• Graph a Line Given a Point and the Slope Step 1. Plot the given point. Step 2. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 3. Starting at the given point, count out the rise and run to mark the second point. Step 4. Connect the points with a line.

• Slope of a Horizontal Line The slope of a horizontal line, $y=b$, is 0.

• Slope of a vertical line The slope of a vertical line, $x=a$, is undefined

• The slope–intercept form of an equation of a line with slope $m$ and y-intercept, $(0,b)$ is, $y=mx+b$.

• Graph a Line Using its Slope and y-Intercept Step 1. Find the slope-intercept form of the equation of the line. Step 2. Identify the slope and y-intercept. Step 3. Plot the y-intercept. Step 4. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 5. Starting at the y-intercept, count out the rise and run to mark the second point. Step 6. Connect the points with a line.

• Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation. If it only has one variable, it is a vertical or horizontal line.$x=a$ is a vertical line passing through the x-axis at $a$.$y=b$ is a horizontal line passing through the y-axis at $b$. If $y$ is isolated on one side of the equation, in the form $y=mx+b$, graph by using the slope and y-intercept. Identify the slope and y-intercept and then graph. If the equation is of the form $Ax+By=C$, find the intercepts. Find the x- and y-intercepts, a third point, and then graph.

• Parallel lines are lines in the same plane that do not intersect. Parallel lines have the same slope and different y-intercepts. If m${}_{1}$ and m${}_{2}$ are the slopes of two parallel lines then ${m}_{1}={m}_{2}.$ Parallel vertical lines have different x-intercepts.

• Perpendicular lines are lines in the same plane that form a right angle. If ${m}_{1}\,\mathrm{and}\,{m}_{2}$ are the slopes of two perpendicular lines, then ${m}_{1}\cdot{m}_{2}=-1$ and ${m}_{1}=\frac{-1}{{m}_{2}}$. Vertical lines and horizontal lines are always perpendicular to each other.

• To Find an Equation of a Line Given the Slope and a Point Step 1. Identify the slope. Step 2. Identify the point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 4. Write the equation in slope-intercept form.

• To Find an Equation of a Line Given Two Points Step 1. Find the slope using the given points. Step 2. Choose one point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 4. Write the equation in slope-intercept form.

• To Write and Equation of a Line If given slope and y-intercept, use slope–intercept form $y=mx+b$. If given slope and a point, use point–slope form $y-{y}_{1}=m(x-{x}_{1})$. If given two points, use point–slope form $y-{y}_{1}=m(x-{x}_{1})$.

• To Find an Equation of a Line Parallel to a Given Line Step 1. Find the slope of the given line. Step 2. Find the slope of the parallel line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 5. Write the equation in slope-intercept form.

• To Find an Equation of a Line Perpendicular to a Given Line Step 1. Find the slope of the given line. Step 2. Find the slope of the perpendicular line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$. Step 5. Write the equation in slope-intercept form.

• To Graph a Linear Inequality Step 1. Identify and graph the boundary line. If the inequality is $\le\mathrm{or}\ge$, the boundary line is solid. If the inequality is < or >, the boundary line is dashed. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality? Step 3. Shade in one side of the boundary line. If the test point is a solution, shade in the side that includes the point. If the test point is not a solution, shade in the opposite side.

##

Review Exercises

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

Verify Solutions to an Equation in Two Variables

In the following exercises, which ordered pairs are solutions to the given equations?

Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

Recognize the Relation Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

1. ⓐ Is the ordered pair a solution to the equation?

2. ⓑ Is the point on the line?

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph each equation.

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

Identify the x- and y-Intercepts on a Graph

In the following exercises, find the x- and y-intercepts.

Find the x- and y-Intercepts from an Equation of a Line

In the following exercises, find the intercepts of each equation.

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

Use $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

Solve Slope Applications

In the following exercises, solve these slope applications.

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y=mx+b$.

Identify the Slope and y-Intercept from an Equation of a Line

In the following exercises, identify the slope and y-intercept of each line.

Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y-intercept.

In the following exercises, determine the most convenient method to graph each line.

Graph and Interpret Applications of Slope–Intercept

Use Slopes to Identify Parallel Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.

Use Slopes to Identify Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.

Find an Equation of the Line Given the Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

Find an Equation of the Line Given the Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Find an Equation of the Line Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

Find an Equation of a Line Parallel to a Given Line

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

Find an Equation of a Line Perpendicular to a Given Line

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

Graph Linear Inequalities

In the following exercises, graph each linear inequality.

##

Find the slope of each line shown.

Graph the line for each of the following equations.

Find the equation of each line. Write the equation in slope–intercept form.

Graph each linear inequality.

1. 1. ⓐ $(4,3)$

2. ⓑ $(-4,3)$

3. ⓒ $(-4,-3)$

4. ⓓ $(4,-3)$

2. 1. ⓐ $(2,\frac{3}{2})$

2. ⓑ $(3,\frac{4}{3})$

3. ⓒ $(\frac{1}{3},-4)$

4. ⓓ $(\frac{1}{2},-5)$

3. $y=6x-2$

1. ⓐ $(1,4)$

2. ⓑ $(\frac{1}{3},0)$

3. ⓒ $(6,-2)$

4. $y=-\frac{1}{2}x+3$

5. $3x+2y=6$

1. $x+y=-4$

2. $y=-x-1$

3. $y=\frac{2}{3}x-1$

ⓐ $(0,-1)$

ⓑ $(3,1)$

ⓒ $(-3,-3)$

ⓓ $(6,4)$

4. $y=-3x$

5. $x-y=6$

1. $3x-2y=6$

2. $x=3$

3. $y=\frac{4}{3}x$ and $y=\frac{4}{3}$

4. $x-y=-1$

5. $2x+3y=12$

1. $y=3x$

2. $x+y=-2$

3. $2x-y=5$

4. $y=2x$

5. $\frac{3}{2}$

1. $-\frac{1}{2}$

2. $x=5$

3. $(3,5),(4,-1)$

4. $(2,1),(4,6)$

5. $(-3,4)$; $m=-\frac{1}{3}$

1. y-intercept 1; $m=-\frac{3}{4}$

2. A mountain road rises 50 feet for a 500-foot run. What is its slope?

3. $y=-\frac{2}{3}x+4$

4. $y=\frac{5}{3}x-6$

5. $4x-5y=8$

1. $y=-x-1$

2. $4x-3y=12$

3. $y=-3$

4. $x-y=2$

5. $y=\frac{3}{4}x-1$

1. Marjorie teaches piano. The equation $P=35s-250$ models the relation between her weekly profit, P, in dollars and the number of student lessons, s, that she teaches.

1. ⓐ Find Marjorie’s profit for a week when she teaches no student lessons.

2. ⓑ Find the profit for a week when she teaches 20 student lessons.

3. ⓒ Interpret the slope and P–intercept of the equation.

4. ⓓ Graph the equation.

2. $2x-y=8;\,x-2y=4$

3. $3x-2y=5;2x+3y=6$

4. slope $-5$ and $y\mathrm{-intercept}$$(0,-3)$

5. slope $-2$ and $y\mathrm{-intercept}$$(0,0)$

1. $m=\frac{3}{5}$, point $(10,6)$

2. $m=-2$, point $(-1,-3)$

3. $(7,1)$ and $(5,0)$

4. $(5,2)$ and $(-1,2)$

5. line $2x+5y=-10$, point $(10,4)$

1. line $y=-5$, point $(-4,3)$

2. line $2x-3y=9$, point $(-4,0)$

3. line $x=-5$ point $(2,1)$

4. Determine whether each ordered pair is a solution to the inequality $x+y>4$:

1. ⓐ $(6,1)$

2. ⓑ $(-3,6)$

3. ⓒ $(3,2)$

4. ⓓ $(-5,10)$

5. ⓔ $(0,0)$

5. Write the inequality shown by the graph with the boundary line $y=\frac{2}{3}x-3$.

1. Write the inequality shown by the shaded region in the graph with the boundary line $x-2y=6.$

2. Graph the linear inequality $y<-\frac{1}{4}x+3$.

3. Graph the linear inequality $3x+2y>10$.

4. Graph the linear inequality $y<6$.

5. Which of the given ordered pairs are solutions to the equation $3x-y=6$?

1. ⓐ $(3,3)$

2. ⓑ $(2,0)$

3. ⓒ $(4,-6)$

1. Find the x- and y-intercepts of the equation $4x-3y=12$.

2. Find the slope of the line between the points $(5,2)$ and $(-1,-4)$.

3. $y=\frac{5}{3}x-1$

4. $x-y=2$

5. $y=2$

1. slope $-\frac{3}{4}$ and y-intercept $(0,-2)$

2. containing $(10,1)$ and $(6,-1)$

3. perpendicular to the line $y=\frac{5}{4}x+2$, containing the point $(-10,3)$

4. $y>\frac{3}{2}x+5$

5. $y\le-5x$